Combine 1 cup sugar and 1/2 cup water in a heavy saucepan; cook over low heat 10 minutes or until sugar caramelizes, tipping pan to incorporate mixture. Pour evenly into 8 (4-ounce) custard cups.
Whisk together eggs, egg yolks, and remaining 1/2 cup sugar until blended. Gradually add warm milk, whisking constantly; stir in vanilla. Pour mixture into prepared custard cups. Cover each with aluminum foil; place in a jellyroll pan. Add hot water to pan to a depth of 1/4 to 1/2 inch.
Bake at 325° for 1 hour and 10 minutes or until a knife inserted in center comes out clean. Remove custard cups from water; uncover. Cool in cups on wire rack. Cover and chill 3 hours.
Run a knife around edge of custard to loosen; invert each onto a dessert plate.
Note: Custard can also be made in a 9-inch cakepan. Caramelize sugar in cakepan instead of saucepan.